```Date: Mar 18, 2004 11:03 PM
Author: Tim Brauch
Subject: Re: Hex Win Proof?

w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote innews://716e06f5.0403181938.72a82f90@posting.google.com: > It is an old theorem that in Hex, once the board has been completely> filled in with two colours, there *must* be a winning path for one> or other of them.> > Now, I can prove this easily enough mathematically, but I'm wondering> if there is a simple proof, or proof outline, that would be> understandable and reasonably convincing to the intelligent layman.> > Can anyone help out please?> Here's what I'm thinking...Suppose you have red going top-bottom and blue going left-right.  If red does not win, then there must be a path that divides the board into to pieces, a top and a bottom piece.  Red cannot be in any position in that path, so it must be blue.  Thus blue wins.  Rotate pi/2 and switch colors.  QED - Tim-- Timothy M. BrauchGraduate StudentDepartment of MathematicsWake Forest Universityemail is:news (dot) post (at) tbrauch (dot) com
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